Question 1

Find the unknown value.
-$\log _ { a } 64 = 2$

Accepted Answer

A)  $- \frac { 1 } { 8 }$ 
B) -8 
C)  $\frac { 1 } { 8 }$ 
D) 8 
A)  $- \frac { 1 } { 8 }$ 
B) -8 
C)  $\frac { 1 } { 8 }$ 
D) 8

Question 2

Graph the function.
-$f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x }$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 3

Use the change of base formula to find the value of the following logarithm. Do not round logarithms in the change of
base formula. Write the answer rounded to the nearest ten-thousandth.
-$$\log _ { 16 } 48.4$$

Accepted Answer

A) 0.4807 
B) 1.3992 
C) 2.8890 
D) 0.7147 
A) 0.4807 
B) 1.3992 
C) 2.8890 
D) 0.7147

Question 4

Use a calculator to solve the equation. Round the answer to the nearest hundredth.
-$$7 ^ { x } = 63$$

Accepted Answer

A) 2.13 
B) 1.81 
C) -2.13 
D) 0.47 
A) 2.13 
B) 1.81 
C) -2.13 
D) 0.47

Question 5

Find the number N. Round N to six decimal places.
-log N = 1.2955

Accepted Answer

A) 1.347566 
B) 0.273761 
C) 19.746949 
D) 0.050641 
A) 1.347566 
B) 0.273761 
C) 19.746949 
D) 0.050641

Question 6

Find the unknown value.
-$\log _ { 7 } \frac { 1 } { 343 } = y$

Accepted Answer

A) -49 
B) 49 
C) 3 
D) -3 
A) -49 
B) 49 
C) 3 
D) -3

Question 7

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth.
-$$\log ( 2 + x ) - \log ( x - 3 ) = \log 2$$

Accepted Answer

A)  $\frac { 3 } { 2 }$ 
B) 8 
C) -8 
D) no solution 
A)  $\frac { 3 } { 2 }$ 
B) 8 
C) -8 
D) no solution

Question 8

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth.
-$$\log _ { 9 } ( 3 x + 2 ) = \log _ { 9 } ( 3 x + 7 )$$

Accepted Answer

A) 0 
B) 5 
C)  $\frac { 9 } { 5 }$ 
D) no solution 
A) 0 
B) 5 
C)  $\frac { 9 } { 5 }$ 
D) no solution

Question 9

Determine whether the function is a one-to-one function.
-$$y = \sqrt { x + 5 } , x \geq - 5$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 10

Use properties of logarithms to expand the logarithmic expression as much as possible.
-$\log _ { 6 } \sqrt [ 4 ] { y }$

Accepted Answer

A)  $4 \log _ { 6 } y$ 
B)  $\frac { 1 } { 4 } \log _ { 6 } \mathrm { y }$ 
C)  $\frac { 1 } { 4 } \log _ { 6 } \sqrt [ 4 ] { y }$ 
D)  $\frac { 1 } { 6 } \log _ { 4 } \mathrm { y }$ 
A)  $4 \log _ { 6 } y$ 
B)  $\frac { 1 } { 4 } \log _ { 6 } \mathrm { y }$ 
C)  $\frac { 1 } { 4 } \log _ { 6 } \sqrt [ 4 ] { y }$ 
D)  $\frac { 1 } { 6 } \log _ { 4 } \mathrm { y }$

Question 11

For the given functions f and g , find the indicated value.
-$f ( x ) = x ^ { 2 } + 6 x , \quad g ( x ) = x + 2$
$( g \circ f ) ( 4 )$

Accepted Answer

A) 42 
B) 44 
C) 240 
D) 72 
A) 42 
B) 44 
C) 240 
D) 72

Question 12

Solve the equation.
-$\ln \left( x ^ { 2 } - 4 \right) - \ln ( x + 2 ) = \ln 1$

Accepted Answer

A)  $\pm 2$ 
B) 3 
C)  $\pm \sqrt { 5 }$ 
D) 2 
A)  $\pm 2$ 
B) 3 
C)  $\pm \sqrt { 5 }$ 
D) 2

Question 13

Solve the problem.
-Find out how long it takes a $3300 investment to double if it is invested at 9% compounded monthly. Round to the nearest tenth of a year. Use the formula $$A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$$ .

Accepted Answer

A) 7.9 yr 
B) 7.5 yr 
C) 7.7 yr 
D) 8.1 yr 
A) 7.9 yr 
B) 7.5 yr 
C) 7.7 yr 
D) 8.1 yr

Question 14

Graph the function.
-$y = \log _ { 1 / 5 } x$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 15

Solve the problem.
-The function $f ( x ) = 1 + 1.3 \ln ( x + 1 )$ models the average number of free-throws a basketball player can make consecutively during practice as a function of time, where x is the number of consecutive days the basketball
Player has practiced for two hours. After 46 days of practice, what is the average number of consecutive free
Throws the basketball player makes?

Accepted Answer

A) 10 consecutive free throws 
B) 9 consecutive free throws 
C) 6 consecutive free throws 
D) 7 consecutive free throws 
A) 10 consecutive free throws 
B) 9 consecutive free throws 
C) 6 consecutive free throws 
D) 7 consecutive free throws

Question 16

Solve the problem.
-The Richter Scale measures the magnitude M of an earthquake. An earthquake whose seismographic reading measures x millimeters 100 kilometers from the epicenter has magnitude M given byven by $M ( x ) = \log \left( \frac { x } { 10 ^ { - 3 } } \right)$ . Give Giv
The magnitude of an earthquake that resulted in a seismographic reading of 68,549 millimeters 100 kilometers
From its epicenter. Round to the nearest tenth.

Accepted Answer

A) 1.8 
B) 6.8 
C) 8.8 
D) 7.8 
A) 1.8 
B) 6.8 
C) 8.8 
D) 7.8

Question 17

Evaluate.
-$$7 ^ { \log _ { 7 } 5 } + 8 ^ { \log _ { 8 } 4 }$$

Accepted Answer

A)  $15 \log _ { 15 } 9$ 
B)  $56 \log _ { 56 } 20$ 
C) 9 
D) 67 
A)  $15 \log _ { 15 } 9$ 
B)  $56 \log _ { 56 } 20$ 
C) 9 
D) 67

Question 18

Write the equation in logarithmic form.
-$2 ^ { - 2 } = \frac { 1 } { 4 }$

Accepted Answer

A)  $\log _ { - 2 } \frac { 1 } { 4 } = 2$ 
B)  $\log _ { 2 } \frac { 1 } { 4 } = - 2$ 
C)  $\log _ { 1 / 4 } 2 = - 2$ 
D)  $\log _ { 2 } - 2 = \frac { 1 } { 4 }$ 
A)  $\log _ { - 2 } \frac { 1 } { 4 } = 2$ 
B)  $\log _ { 2 } \frac { 1 } { 4 } = - 2$ 
C)  $\log _ { 1 / 4 } 2 = - 2$ 
D)  $\log _ { 2 } - 2 = \frac { 1 } { 4 }$

Question 19

For the given functions f and g , find the indicated composition.
-$$\begin{array} { l } 
f ( x ) = \frac { 7 } { x - 5 } , \quad g ( x ) = \frac { 3 } { 4 x } \
( f \circ g ) ( x )
\end{array}$$

Accepted Answer

A)  $\frac { 28 x } { 3 - 20 x }$ 
B)  $\frac { 28 x } { 3 + 20 x }$ 
C)  $\frac { 3 x - 15 } { 28 x }$ 
D)  $\frac { 7 x } { 3 - 20 x }$ 
A)  $\frac { 28 x } { 3 - 20 x }$ 
B)  $\frac { 28 x } { 3 + 20 x }$ 
C)  $\frac { 3 x - 15 } { 28 x }$ 
D)  $\frac { 7 x } { 3 - 20 x }$

Question 20

Determine whether the given functions are inverses of each other.
-$$f ( x ) = \frac { x - 4 } { 4 } , \quad g ( x ) = 4 x + 4$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Find the unknown value. - $\log _ { a } 64 = 2$

Graph the function. - $f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x }$ $Graph the function. - f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x }$

Use the change of base formula to find the value of the following logarithm. Do not round logarithms in the change of base formula. Write the answer rounded to the nearest ten-thousandth. - $\log _ { 16 } 48.4$

Use a calculator to solve the equation. Round the answer to the nearest hundredth. - $7 ^ { x } = 63$

Find the number N. Round N to six decimal places. -log N = 1.2955

Find the unknown value. - $\log _ { 7 } \frac { 1 } { 343 } = y$

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - $\log ( 2 + x ) - \log ( x - 3 ) = \log 2$

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - $\log _ { 9 } ( 3 x + 2 ) = \log _ { 9 } ( 3 x + 7 )$

Determine whether the function is a one-to-one function. - $y = \sqrt { x + 5 } , x \geq - 5$

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { 6 } \sqrt [ 4 ] { y }$

For the given functions f and g , find the indicated value. - $f ( x ) = x ^ { 2 } + 6 x , \quad g ( x ) = x + 2$ $( g \circ f ) ( 4 )$

Solve the equation. - $\ln \left( x ^ { 2 } - 4 \right) - \ln ( x + 2 ) = \ln 1$

Solve the problem. -Find out how long it takes a $3300 investment to double if it is invested at 9% compounded monthly. Round to the nearest tenth of a year. Use the formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ .

Graph the function. - $y = \log _ { 1 / 5 } x$ $Graph the function. - y = \log _ { 1 / 5 } x$

Evaluate. - $7 ^ { \log _ { 7 } 5 } + 8 ^ { \log _ { 8 } 4 }$

Write the equation in logarithmic form. - $2 ^ { - 2 } = \frac { 1 } { 4 }$

For the given functions f and g , find the indicated composition. - f(x)=,g(x)= (f\circg)(x)

Determine whether the given functions are inverses of each other. - $f ( x ) = \frac { x - 4 } { 4 } , \quad g ( x ) = 4 x + 4$

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

Filters

Exam 9: Exponential and Logarithmic Functions

Find the unknown value. - log⁡a64=2\log _ { a } 64 = 2loga​64=2

Graph the function. - f(x)=(14)xf ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x }f(x)=(41​)x

Use the change of base formula to find the value of the following logarithm. Do not round logarithms in the change of base formula. Write the answer rounded to the nearest ten-thousandth. - log⁡1648.4\log _ { 16 } 48.4log16​48.4

Use a calculator to solve the equation. Round the answer to the nearest hundredth. - 7x=637 ^ { x } = 637x=63